Calculating rate of return

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Arate of return is a measure of the increase (or decrease) in an investment
over a period of time. You invest to earn a return in the form of
income (interest and dividends) and/or capital appreciation (when
the price of the investment sold is higher than the purchase price).
Some investments, such as savings accounts and CDs, offer only income
with no capital appreciation; others, such as common stock,
offer the potential for capital appreciation and may or may not pay
dividends. If the price of a stock declines below the purchase price
and you sell the stock, you have a capital loss. The simple definition
of total return includes income and capital gains and losses.

Calculating a return is important because it measures the
growth or decline of your investment, and it provides a yardstick
for evaluating the performance of your portfolio against your objectives.
You can calculate the total rate of return as follows:

You should include spreads and commissions in the calculation.
For example, if you bought a stock at the beginning of the year for
$1,000 (including the commission), sold it at the end of the year for
$1,500 (net proceeds received after deducting the commission), and
earned a dividend of $50, the rate of return is 55 percent:

Rate of return = [(1,500 - 1,000) + 50]/1,000 = 55%

This rate of return is simple and easy to use, but it is somewhat
inaccurate if the investment is held for a long period of time
because the time value of money is not taken into account. The time
value of money is a concept that recognizes that a dollar today is
worth more in the future because of its earnings potential. For
example, if you invested a dollar at 5 percent for one year, it would
be worth $1.05 at the end of one year. Similarly, if you expect to
receive a dollar at the end of one year, it would have a present
value of less than a dollar (now).

This simple average rate of return of 55 percent does not take
into account the earnings capacity of the interest. In other words,
you would reinvest the $50 of dividends you received, which would
increase the rate of return above 55 percent owing to compounding
of the interest.

Using the time value of money to calculate the rate of return
gives you a more accurate rate-of-return figure. However, it is more
difficult to calculate because the rate of return on a stock equates the
discounted cash flows of future dividends and the stock’s expected
sale price to the stock’s current purchase price. This formula works
better for bonds than for common stocks because the coupon rate
for bonds is generally fixed, whereas dividend rates on common
stocks fluctuate (and you therefore need to make assumptions).
When companies experience losses, they might reduce their dividend
payments, as Ford Motor Company did to preserve its cash in
2006. If a company’s earnings increase, the company might increase
the amount of its dividend payments. The future sale price of a
stock has even less certainty. Bonds are retired at their par price
($1,000 per bond) at maturity; but when a stock eventually is sold,
the future sale price is anyone’s guess.

How do you calculate a return for a portfolio? It is useful to
be able to compute a return for a portfolio of investments. The
following example illustrates the steps to determine such a return.
The portfolio has five stocks with the following returns:

Stock

Return

A

7.5%

B

6.2%

C & D

2.0%

E

-3.1%

The returns for the stocks are weighted and then summed to
give the portfolio weighted average return:
To be able to compare your portfolio return with the return of
the market, you need to be able to determine your return accurately.

Stock

Weighting

Rate

Weighted Average Return

A

1/5

*

0.075

=

1.5%

B

1/5

*

0.062

=

1.24%

C & D

2/5

*

0.02

=

0.8%

E

1/5

*

-0.031

=

-0.62%

2.92%

This process may not be easy if you add funds to purchase securities
and withdraw funds during the holding period. You may recall
that a few years ago the Beardstown Ladies Investment Club had
a problem calculating its returns accurately. The members claimed
to have earned average annual returns in the low 20 percent range
for an extended period, beating annual market averages, only to
find that they had computed their returns incorrectly. In fact, an
audit by a prominent accounting firm showed that their average
annual returns were in single digits during that same period.
For a portfolio where you have not added or withdrawn
any funds, the simple holding-period return discussed earlier is
sufficient:

Table 5–1 illustrates how to calculate a return for a portfolio
where funds have been added and withdrawn.

Table 5-1
Measuring a Portfolio Return with Additions and Withdrawals
to the Portfolio
If you had $100,000 in your portfolio at the beginning of the year, and at the end of
the year your portfolio had increased to $109,000, you had a 9 percent return
[($109,000 -100,000)/100,000].
For additions and withdrawals during the year, the holding-period return for a portfolio
is calculated as follows:
For example, a portfolio that began with $110,500 at the beginning of the year,
received dividends of $8,600 and capital gains of $12,000, suffered unrealized
losses of $6,000 during the year, had new funds of $10,000 added at the beginning
of April, and had $4,000 withdrawn at the end of October had an annual
return of 12.44 percent:
This portfolio earned a 12.44 percent return before taxes and can be compared with
a comparable benchmark index for the same period of time.